An analytical approach to planar ionization fronts in dense gases

The analytical theory of 1D propagating ionization fronts is developed in the fluid approximation. Electron diffusion and thermal conductivity are neglected. It is shown that the applied field shielding process by the space charge can be described in the surface charge approximation with satisfactory accuracy. This process can be subdivided into two different stages. During the first stage the surface charge density increases mainly due to ionization. In the anode-directed (negative) fronts after this stage the ionization is switched off, and the ion density remains frozen at the fixed level n∞. Afterwards the field shielding is due to a shift of the electron density profile, which results in expansion of the space charge region. Formation of the cathode-directed (positive) front is analysed for the case when the primary electrons are supplied by the electron emission from the cathode. Relatively simple scaling laws for the front velocity and plasma characteristics in various spatial regions and during different evolution stages are derived. The results agree satisfactorily with simulations.